Modern pricing models - Essay Example

In every financial modeling for pricing options, the main purpose of applying the financial model is through the determination of correct prices after evaluating a number of generated predictions. Similarly, the same case applies to the geometric Brownian motion model, which is an assumption of stock price behavior used by various models through simulations to determine the future prices of stock, especially in the options and stock prices for investors. As such, investors get to learn how best to place their investments judging from the future expected price changes of a given stock price or of an option.

         A geometric Brownian motion (GBM), or an exponential Brownian motion, refers to a stochastic process that runs continuously over time in which case the logarithm of the randomly varying quantity follows a Wiener process, or the Brownian motion with a drift. The Brownian motion is a significant example of the stochastic processes that satisfy a stochastic differential equation (SDE). Most applications of Brownian motion incorporate, in particular, mathematical finance, especially in consideration of the model stock prices, such as is the case with Black-Scholes model.

As such, the geometric Brownian motion is a core building block of modern finance. This is particularly in the case of the Black Scholes model whereby the underlying stock price is assumedly in line with the principles and expectations of the GBM dynamics.